Is the error function known or unknown?
In deep learning, the error function is sometimes known as loss function or cost function (but I do not exclude the possibility that these terms/expressions have also been used to refer to different although related functions, so you should take into account your context).
In statistical learning theory, the function that you want to minimize is known as expected risk
\begin{align}
R(\theta)
&amp;=
\int L(y, f_{\theta}(x)) d P(x, y) \\
&amp;=
\mathbb{E}_{P(x, y)} \left[ L(y, f_{\theta}(x)) \right],
\end{align}
where $\theta$ are the parameters of your model $f$, and the function that you actually minimize is the empirical risk given the dataset $D = \{ (x_i, y_i) \}_{i=1}^n$,
$$
R_{\mathrm{emp}}(\theta)=\frac{1}{n} \sum_{i=1}^{n}L(y_i, f_{\theta}(x_i)),
$$
which is a generalization of the commonly used cost functions, such as mean squared error (MSE) or binary cross-entropy. For example, in the case of MSE, $L = \left(y_{i}-f_\theta(x_i)\right)^{2}$, which can be called the loss function (though this terminology may not be standard).
You optimize the empirical risk, a proxy for the expected risk, because the expected risk is incomputable (given that $P(x, y)$ is generally unknown), so, in this sense, the expected risk is unknown.
If you use the term error function to refer to the expected risk, then, yes, the error function is typically unknown, but error function is typically used to refer to an instance of the empirical risk, so, in that case, it is known and computable.
Note that I purposely used the term loss function above to refer to $L$ and the term cost function to refer to the empirical risks, such as the MSE (i.e., in this case, I did not use loss function and cost function as synonyms), which shows that terminology is not always used consistently, so take into account your context.